In a field of error correction, a phenomenon that a decreasing rate of an error rate is deteriorated in a high SNR region as compared to a low SNR (signal to noise power ratio) region. This phenomenon is referred to as an error-floor phenomenon. The error-floor phenomenon is a crucial obstacle for many communication systems and memory systems. In general, when two received words have errors completely independent from each other, it is possible to decrease the error rate in an error-floor by automatic repeat request. However, in some systems, an error position of a repeatedly transmitted received word has correlation with the error position of a first received word. In such system, it is difficult to decrease the error rate in the error-floor by the automatic repeat request.